The first step to building the rack is to work on the two sides. These are made from 4/4 (1-inch thick) stock of the species of your choice. Oak and Maple make beautiful choices if the unit is to be stained, while Poplar is terrific if you intend to paint the rack.
Cut each of the two pieces of 4/4 stock to 6" x 9-3/4".
Next, you'll need to cut four notches in each piece to accommodate the front and back of the unit. These notches are cut on the long (9-3/4") edges, 3/4" in from each end. The notches will be 1/2" deep and 3/4" wide (the width of the 1x stock used for the front and back).
To cut the notches, set up a stacked dado set in either your Table Saw or Radial Arm Saw to 3/4-inch in thickness, and set the depth to 1/2-inch.
Because you'll be cutting the sides on edge, it would be safest and smoothest to clamp the two sides together and cut the dadoes on both pieces of stock at the same time. If you plan on building more than one set of this wine rack, try cutting four sides at a time. If using a table saw, be sure to use a miter gauge to guide the stock - do not use the fence, as the stock could bind against the fence as it is run through the saw.
Once you have the four dadoes cut, move onto the cutout within the sides. You can either cut two 2-1/4" holes and clean the stock between with a jigsaw, or simply cut the entire cutout with the jigsaw. The edges of the holes will be 2-1/8" in from the edges (along the center line), with the entire width of the cutout measuring 5-1/2", as shown in the plan diagrams (which can be downloaded from the first page of this article.
The last woodworking step on the side panels is to cut a 3/8" diameter hole (about 1/4" deep) centered in each of the four dadoes to accommodate the dowels in a later step.